\(\displaystyle \text{Let } x = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \text{ and } A = \begin{bmatrix} -1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1 \end{bmatrix}\). For \( k \in \mathbb{N} \), if \( X' A^{k} X = 33 \), then \( k \) is equal to __________.
